Has anyone had any experience with Uschi van der Rosten .001mm rigging thread for rigging 1/350 WW2-era ships? I had been using EZ-line, but found it reacts poorly to CA glue; gets noticeable flat spots; and the covering on the thread separates and looks ragged after painting.

Same stuff. But I've been modeling with Berkshire industries EZ line and Ushi for several years now (primarily for WWI aircraft rigging, but also several ship models for commission, and I also used EZ line for model RR projects 20 years ago), and I've never had a problem like you are describing. The only problems I've noticed is if I stretch it too tightly, and glue it on the end, it does have a tendency to split. What I've been doing is stretching it an inch or too past the point I want to glue it, and use it a needle with just a slight amount of CA to touching the place I want it glued. I also use a very fine pair of cross-tip tweezers to hold the line with. I do notice it takes enamel paint better than acrylics (it takes Tamiya paints ok). I've also used colored paint pens and black permanent markers, which also work OK. It sounds like you might be stretching it too tightly
VR, Russ